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Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 1, Pages 59–74 (Mi izv8731)  

Existence theorems for a class of systems involving two quasilinear operators

D.-P. Covei

The Bucharest Uviversity of Economic Studies, Romania

Abstract: In this paper, we study the existence of positive radial solutions for a class of quasilinear systems of the form
$$ \begin{cases} \Delta_{\phi_1}u=a_1(|x|)f_1(v),
\Delta_{\phi_2}v=a_2(|x|)f_2(u), \end{cases} \quad x\in \mathbb{R}^N, \quad N\ge 3, $$
where $\Delta_{\phi}w:=\operatorname{div}(\phi(|\nabla w|)\nabla w)$, under appropriate conditions on the functions $\phi_1$, $\phi_2$, the weights $a_1$, $a_2$ and the non-linearities $f_1$, $f_2$. The conditions imposed for the existence of such solutions are different from those in previous results.

Keywords: partial differential equations, cooperative systems, linear systems, non-linear systems, methods of approximation.

DOI: https://doi.org/10.4213/im8731

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English version:
Izvestiya: Mathematics, 2019, 83:1, 49–64

Bibliographic databases:

UDC: 517.956
MSC: 34B15, 34B18, 35B08, 35B09, 35B44, 35M30
Received: 01.11.2017

Citation: D.-P. Covei, “Existence theorems for a class of systems involving two quasilinear operators”, Izv. RAN. Ser. Mat., 83:1 (2019), 59–74; Izv. Math., 83:1 (2019), 49–64

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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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